Bloodlines is popular application for Facebook.
It's a game where you take on the role of a recently turned vampire.

The only way to progress through the game, generally, is to have lots of "clan members". Most often, your clan members are people you don't really know in real life, but you friend on facebook anyway for the sake of advancing in the game (you have to friend someone on facebook for them to join your clan).

There is also a system of "favors" that are given by the "mysterious cabal". Favors can be earned through achievements (such as growing your clan to a certain number of people);
Doing long, boring, and sometimes expensive sponsorship offers, or buying them straight out for a considerable sum of money.

Its players span many countries, and age groups, all of whom are hopelessly addicted to the game.